I get a lot of questions about the formula for the canonical form of a quadratic function introduced in my Course on Indefinite Integrals. Why is there a^2? Let me explain.
There are times in life when the region of integration in a double integral is an ellipse…. What do we do then?
In indefinite rational integrals, as we know, it is often necessary to factorize the denominator of the integrand and further decompose it into simple fractions. However, factorization itself can often be tricky.
In rational indefinite integrals, there’s often a need to factorize the quadratic trinomial ax^2 + bx + c. We do this using the formula ax^2 + bx + c = a(x – x1)(x – x2), which works when Delta is greater than 0. But what happens when Delta is precisely 0?
We’ve gotten used to applying the formula with arctan tgx in “clean” integral situations. What if there are expressions that seem to have no “neat” root? Discover methods for solving indefinite integrals with the arctan function.
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